A162594 Differences of cubes: T(n,n) = n^3, T(n,k) = T(n,k+1) - T(n-1,k), 0 <= k < n, triangle read by rows.

0, 1, 1, 6, 7, 8, 6, 12, 19, 27, 0, 6, 18, 37, 64, 0, 0, 6, 24, 61, 125, 0, 0, 0, 6, 30, 91, 216, 0, 0, 0, 0, 6, 36, 127, 343, 0, 0, 0, 0, 0, 6, 42, 169, 512, 0, 0, 0, 0, 0, 0, 6, 48, 217, 729, 0, 0, 0, 0, 0, 0, 0, 6, 54, 271, 1000, 0, 0, 0, 0, 0, 0, 0, 0, 6, 60, 331, 1331

Offset

0,4

Comments

T(n,n) = A000578(n);

T(n,n-1) = A003215(n-1), n > 0;

T(n,n-2) = A008588(n-2), n > 1;

T(n,n-3) = A010722(n-3), n > 2;

T(n,n-j) = A000004(n-j), 4 <= j <= n;

for n > 2: sum of n-th row = (n+1)^3.

Links

G. C. Greubel, Rows n = 0..99 of triangle, flattened

Example

Triangle begins:
  0,
  1,  1,
  6,  7,  8,
  6, 12, 19, 27,
  0,  6, 18, 37, 64,
  0,  0,  6, 24, 61, 125,
  ...

Mathematica

T[n_, n_] := n^3; T[n_, k_] := T[n, k] = T[n, k + 1] - T[n - 1, k]; Table[T[n, k], {n, 0, 15}, {k, 0, n}] // Flatten (* G. C. Greubel, Jul 04 2018 *)

Prog

(PARI) T(n, k) = if (k==n, n^3, T(n, k+1) - T(n-1, k));
tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n, k), ", ")); print); \\ Michel Marcus, Jul 05 2018

Crossrefs

Cf. A162593 (differences of squares).

Sequence in context: A085661 A265276 A286474 * A229948 A198124 A120207

Adjacent sequences: A162591 A162592 A162593 * A162595 A162596 A162597

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Jul 07 2009

Status

approved